Grade 12Algebra

if slope of one of the lines given by ax 2+2hxy+by 2=0 is three times the other then the condition for h is

rushikesh kale

10 Years agoGrade 12

10 Years ago

divide d given equation by $x^{2}$ and let y/x be slope m hence we get $bm^{2}+2hm+a=0$

nw, let d roots of this equation be $m_{1} , m_{2}$ as given $m_{1} =3 m_{2}$ nw SOR = m1 + m2=-2h/b=4m2

POR=m1m2= $3 m_{2}^{2}$ = a/b therefore, $m_{2}=\sqrt{a/3b}$ , $m_{2}=\sqrt{a/3b}= - h/2b \therefore h=-2\sqrt{ab/3}$

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